Reading & Writing in the Disciplines
Blended Learning: Using Technology to Learn Math Concepts
Leon Young uses technology in the classroom to facilitate communication among peers and to support differentiated instruction of small learning groups.
Teacher: Leon Young
School: REALM Charter School, Berkeley, CA
Discipline: Mathematics (Algebra 1)
Lesson Topic: Arithmetic sequences
Lesson Month: January
Number of Students: 23
Other: REALM, the Revolutionary Education and Learning Movement, is a project-based and technology-rich charter school.
Featured Lesson’s Student Goals:
- Content objectives – Evaluate arithmetic sequences by finding the common difference; determine whether a sequence is an arithmetic sequence
- Literacy/language objectives – Gain confidence in speaking and practice communicating knowledge clearly
- Engagement/interaction objectives – Collaborate with peers to solve problems and teach each other
Common Core State Standards for Mathematics
Make sense of problems and persevere in solving them.
Construct viable arguments and critique the reasoning of others.
Common Core State Standards for English Language Arts & Literacy in History/Social Studies, Science, and Technical Subjects
Determine the meaning of symbols, key terms, and other domain-specific words and phrases as they are used in a specific scientific or technical context relevant to grades 6–8 texts and topics.
Integrate quantitative or technical information expressed in words in a text with a version of that information expressed visually (e.g., in a flowchart, diagram, model, graph, or table).
During the Video
Mr. Young keeps his classroom set up for small-group learning. At each station, there is a set of tablet PCs (one for each student), a projector, and an eight-foot whiteboard. The projector can connect to the laptops so that students can project and share their work. There is also a mini Android computer connected to the whiteboard with a switchbox so that students can switch between a laptop and an Android computer.
When students walked in, a warm-up activity was already waiting for them on their board. They worked at the board with their team and explained to each other how they got their answer. Mr. Young discussed where students might see arithmetic sequences in real life, gave some direct instruction about the relevant vocabulary, went over examples of what is and is not an arithmetic sequence, and modeled how to find the common difference and how to use it to find a term in a sequence.
After the direct instruction, students worked in groups to discuss several problems. Mr. Young walked around the room and checked in with each group to see how they were progressing. Students then moved on to independent practice. Each student used their individual tablet PCs to work on arithmetic sequence problems from a website called IXL. Students were encouraged to ask each other questions and help one another.
After the Video
After this lesson, students learned how to write an expression that can describe an arithmetic sequence.
For Mr. Young, a good plan and a good seating chart are the two most important classroom management strategies. He plans his lessons to make them flow as smoothly as possible and tries to remove any barriers that might prevent students from working. He makes things easily accessible, such as offering pencils and paper to students who need them and having everything ready when students walk in (including projecting the agenda and warm-ups onto the boards before students arrive so that they can start working right away). He structures the seating arrangement so that students at different levels are working together and can learn from each other.
Students needed prior knowledge of basic number systems, patterns, and sequences.
Mr. Young tries many approaches to make sure that he reaches different types of learners. For example, he incorporated PowerPoint direct instruction, group work, and individual practice in the featured lesson. Some days he also uses games and videos to engage students. He arranges the groups to include students of different levels so that they help each other; higher-performing students develop speaking and teaching skills while helping the lower-performing students with math concepts.
Mr. Young works with any group that gets stuck while the others continue on; they can check their answers (on the computers) and move on to the next problem. When students are done with the group practice problems, they start independent practice problems. They can then start working on their homework, which is individualized for each student. Mr. Young always has something lined up for students to do.
During this lesson, students sat in groups of four or five at workstations with tablet PCs and projectors. Students worked in these small groups during the warm-up exercise and during guided practice. They talked out the problems and taught each other, which allowed them to work on speaking skills and expressing themselves clearly. During independent practice, students worked independently but were encouraged to seek help from their peers, if needed.
In general, Mr. Young has students working in small groups on a daily basis. This enables them to learn to collaborate with people who may think differently and practice communicating effectively.
Resources and Tools
- Math notebooks
- Individual tablet PCs
- Projector (one at each group station)
- Whiteboard (one at each group station)
During group collaboration time, Mr. Young moves through the room; he observes how students are progressing and where they are getting stuck. When needed, he jumps in to help a group work through the problem. Students also get immediate feedback from the computer programs that they use.
When students were finished with their IXL practice problems, they showed Mr. Young their scores and he recorded them in his gradebook.
Throughout the year, Mr. Young has tried different tools such as Khan Academy, Buzzmath, Revolution K12, and IXL. Each time he uses a different program in class, he asks students for their opinions about how well it works. He continually develops his curriculum based on student feedback, surveys, and diagnostic tests.
8.1 Reading and Writing in Mathematics
Education experts Jacob Foster, Heather Lynn Johnson, and Magdalene Lampert address the key elements of disciplinary literacy in mathematics education and discuss strategies for its integration into the classroom.